Problem: The value of $\sqrt{37}$ lies between which two consecutive integers ? Integers that appear in order when counting, for example 2 and 3.
Explanation: Consider the perfect squares near $37$ . [ What are perfect squares? Perfect squares are integers which can be obtained by squaring an integer. The first 13 perfect squares are: $ 1,4,9,16,25,36,49,64,81,100,121,144,169$ $36$ is the nearest perfect square less than $37$ $49$ is the nearest perfect square more than $37$ So, we know $36 < 37 < 49$ So, $\sqrt{36} < \sqrt{37} < \sqrt{49}$ So $\sqrt{37}$ is between $6$ and $7$.